6 I DEFINITIONS AND ELEMENTARY FACTS.
7. Use of capital and small letters. In dealing with the properties of homogeneous substances, there are certain quantities, such as the volume, which are proportional to the mass of the substance, and others which are independent of the mass. In designating the former class of quantities we shall use capital letters when they refer to the whole body, and small letters when they refer to the unit of mass. Thus taking the case of volumes, if m is the mass, the whole volume will be called V, and the volume of unit mass v, and the relation connecting all such pairs of quantities will be of the form V=mv.
8. Indicator diagrams. If the pressure p and volume v of a simple substance be taken as coordinates of a point in a plane, then any continuous variation of the state of the substance will be represented by a curve described by the point (v,p). The curves corresponding to isothermal and adiabatic transformations will be called isothermal ^ ' and adiabatic curves. Any diagram
drawn in this way will be called an (& K) indicator diagram.
Taking the pressure p and total volume V as coordinates we observe that since the work done in any
expansion is IpdV it is measured by
the area contained by the arc of the
0 ^ curve in the ( F, p) plane and the two
Fig L bounding ordinates to the axis of V.
9. Cycle. When a system starts from a given state and returns to the same state by passing through a different series of intermediate
states it is said to perform a cycle or undergo a cyclic transformation. For a cyclic transformation of a simple system the indicator diagram will be a closed curve in the (V,p) plane, and the total work done by the body, measured by
the integral ( / j p d V will be represented by the area of the closed curve
Q -—------> described.
Fig. 2. If the axis of p makes with the
axis of Fan angle 90° in the counterclockwise direction this work is evidently positive when the curve is. described in the clockwise direction.